Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses

Ramalingam Sriraman; Asha Nedunchezhiyan

Kybernetika (2022)

  • Volume: 58, Issue: 4, page 498-521
  • ISSN: 0023-5954

Abstract

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In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the n -dimensional Clifford-valued neural network into 2 m n -dimensional real-valued counterparts in order to solve the noncommutativity of Clifford numbers multiplication. Then, we prove the new global asymptotic stability criteria by constructing an appropriate Lyapunov-Krasovskii functionals (LKFs) and employing Jensen’s integral inequality together with the reciprocal convex combination method. All the results are proven using linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the achieved results.

How to cite

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Sriraman, Ramalingam, and Nedunchezhiyan, Asha. "Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses." Kybernetika 58.4 (2022): 498-521. <http://eudml.org/doc/299566>.

@article{Sriraman2022,
abstract = {In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the $n$-dimensional Clifford-valued neural network into $2^mn$-dimensional real-valued counterparts in order to solve the noncommutativity of Clifford numbers multiplication. Then, we prove the new global asymptotic stability criteria by constructing an appropriate Lyapunov-Krasovskii functionals (LKFs) and employing Jensen’s integral inequality together with the reciprocal convex combination method. All the results are proven using linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the achieved results.},
author = {Sriraman, Ramalingam, Nedunchezhiyan, Asha},
journal = {Kybernetika},
keywords = {global stability; T-S fuzzy; Clifford-valued neural networks; Lyapunov--Krasovskii functionals; impulses},
language = {eng},
number = {4},
pages = {498-521},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses},
url = {http://eudml.org/doc/299566},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Sriraman, Ramalingam
AU - Nedunchezhiyan, Asha
TI - Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 4
SP - 498
EP - 521
AB - In this study, we consider the Takagi-Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Clifford-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the $n$-dimensional Clifford-valued neural network into $2^mn$-dimensional real-valued counterparts in order to solve the noncommutativity of Clifford numbers multiplication. Then, we prove the new global asymptotic stability criteria by constructing an appropriate Lyapunov-Krasovskii functionals (LKFs) and employing Jensen’s integral inequality together with the reciprocal convex combination method. All the results are proven using linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the effectiveness of the achieved results.
LA - eng
KW - global stability; T-S fuzzy; Clifford-valued neural networks; Lyapunov--Krasovskii functionals; impulses
UR - http://eudml.org/doc/299566
ER -

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